Possible spoilers~
Well, Pyramid Head had been around way before the events of Silent Hill 2. I'm led to believe that James saw that picture of him in the Historical Society when he was in town with his wife, and associated PH with his guilt and judgement.
I never really thought SH Origins and SH2 had any relation to each other. If anything, it's more related to 1 and 3's story seeing as Alessa is involved..and it's the prequel to 1.
As for 4, yeah it has Walter Sullivan in it, (who was mentioned in a newspaper in SH2) but I just never really wanted to consider it a SH game. :/
That's just my opinion though.